The airline said all passengers have been safely deplaned.
Following the incident in the evening, the operations at the Delhi international airport were impacted for nearly two hours as one of the runways was temporarily shut, sources said.
The plane skidded upon landing on runway 29 and "lost control", they added.
"Our flight 9W 2882, an ATR 72-500, from Dehradun to Delhi... experienced a nose wheel malfunction after landing, resulting in a steering problem," Jet Airways said in a statement.
All "60 guests and 5 crew members have been safely deplaned" and that the aircraft is being towed away for maintenance, the airline said.
A Delhi airport official said the runway was shut for nearly two hours and after the aircraft was towed away, the operations resumed at around 1840 hours.
According to Jet Airways, alternative arrangements are being made for the affected passengers.
An ATR aircraft has a seating capacity for 72 people.
Besides Jet Airways, two other full service carriers Air India and Vistara -- operate from runway 29 at the international airport.